Linked Questions

4 votes
1 answer
146 views

Probability mass function with variable probability? [duplicate]

I would like to calculate the probability of a certain result coming out at least 'x' times in 'n' attempts when the probability of result varies on every attempt; all attempts are independent events. ...
Jorge Riv's user avatar
  • 165
2 votes
1 answer
340 views

Probability distribution for varying probabilities in R [duplicate]

I'd like to plot the probability distribution for a set of binomial trials in R, the catch is that each trial has an independent probability of success (which I have in vector form). So, in R if I ...
ryan's user avatar
  • 21
1 vote
1 answer
282 views

How can I efficiently approximate the sum of Bernoulli random variables for any number of summands in partial sum? [duplicate]

I have almost the same question as: How can I efficiently model the sum of Bernoulli random variables? But: (1) The number of random variables for summation is ~ N=20 (case 1) or N=90 (case 2). (2) $...
Andrey's user avatar
  • 41
1 vote
0 answers
13 views

The probability of at least N positive outcomes where all experiments have different probabilities [duplicate]

Let's say we bet on 10 different soccer matches. The probability of our team winning, for each game, is 0.17, 0.78, 0.41, 0.79, 0.47, 0.08, 0.29, 0.30, 0.35, and 0.54. What is the probability of ...
miroli's user avatar
  • 173
1 vote
0 answers
10 views

General way to describe dot product of N different random variables [duplicate]

I'm a novice to DS, so feel free to correct me. Imagine we have $N$ biased coins each with different probability of getting heads (which are known to us prior). What's the probability of getting $k$ ...
MaxelRus's user avatar
  • 111
43 votes
9 answers
15k views

How can I efficiently model the sum of Bernoulli random variables?

I am modeling a random variable ($Y$) which is the sum of some ~15-40k independent Bernoulli random variables ($X_i$), each with a different success probability ($p_i$). Formally, $Y=\sum X_i$ where $\...
David B's user avatar
  • 1,321
60 votes
5 answers
43k views

Probability distribution for different probabilities

If I wanted to get the probability of 9 successes in 16 trials with each trial having a probability of 0.6 I could use a binomial distribution. What could I use if each of the 16 trials has a ...
Greg's user avatar
  • 803
20 votes
2 answers
44k views

Sum of Bernoulli variables with different success probabilities [duplicate]

Let $x_i$ be independent Bernoulli random variables with success probabilities $p_i$. That is, $x_i=1$ with probability $p_i$ and $x_i=0$ with probability $1-p_i$. Is there a closed expression or an ...
a06e's user avatar
  • 4,552
8 votes
1 answer
9k views

Efficient convolution (in R)

I want to calculate/evaluate the convolution $$g(x)=\int_D f(x-t) \phi(t) dt,$$ where $f$ is a density and $\phi$ is a smooth function with compact support $D$. The convolution is not available in ...
Cook's user avatar
  • 83
2 votes
2 answers
2k views

Distribution of a linear combination of Bernoulli random variables?

I am trying to calculate the expectation of absolute value of a linear combination of independent Bernoulli random variables, $E(|a_1x_1 + a_2x_2 + ...+ a_nx_n|)$. In particular, $(a_1, ..., a_n)$ are ...
Jane's user avatar
  • 23
5 votes
1 answer
660 views

Probability of at least $k$ Bernoulli successes with varying probabilities conditional on an event

Suppose a female in a given species has, on a given year $x$, PMF $Bernoulli(f(x))$ of finding a mate given she doesn't yet have one. Once she finds a mate, she doesn't need another. This same ...
Alexandre's user avatar
  • 210
5 votes
2 answers
257 views

Estimate Number of Party Guests

You are throwing a party and want to know how many guests you can expect. You are inviting $N$ persons, each person has a probability $x_i$, $ 1 \leq i \leq N$ of showing up and $x_i$ is between 0 and ...
r0f1's user avatar
  • 267
1 vote
1 answer
926 views

Probability of completing N events

I'd like to calculate the probability that at least N independent events out of a set of M events complete successfully. Each event Ei has a probability of success of Pi. For example, if there are ...
dmjones's user avatar
  • 13
2 votes
1 answer
542 views

How to obtain the density of a sum of independent discrete random variables?

Let's $X_1, X_2, ..., X_n$, $n=1,2,...$ are independent discrete random variables. It is necessary to find the distribution law of the their sum: $p(k) =P(X_1 + X_2 + ... + X_n = k), k=0, 1, 2, ... $ ...
Nick's user avatar
  • 856
4 votes
2 answers
296 views

Calculate percentiles of probabilistic functions

For easier understanding, let's assume we talk about sport betting. There are 3 independent games with team_A winning with a probability of 70%, 50%, 10% respectively. Each bet has its odds (odds_1, ...
Stergios's user avatar
  • 558

15 30 50 per page